4.1.1: Exercises

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Page ID: 48784

Hannah Seidler-Wright
Chaffey College

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A program at a local community college wants to evaluate its attrition rate, this is the number of semesters a student remains in the program. Over the years, they have established the following probability distribution.

Using what you know about probability distributions, find $P(4)$ and enter it in the table below.

$x=$ the number of semesters a student will remain in the program	0	1	2	3	4	5	6
$P(x)$	0.12	0.18	0.30	0.15		0.10	0.05

Graph the probability histogram. Be sure to label the axes.

Images are created with the graphing calculator, used with permission from Desmos Studio PBC.
Find the probability that a student remains in the program for more than 3 semesters. Use probability notation in your answer.
Find the proportion of students who remain in the program for at most 3 semesters. Use probability notation in your answer.
On average, how long do you expect a student to remain in the program? Include units in your answer.

You set up a booth at a local fund-raising event. The game consists of rolling two six-sided dice. The dice are fair, so each individual roll of one die has a probability of 1/6. Players pay $5 per roll. A player who rolls a 2 or a 3 wins a prize that costs you $3. Players who roll an 11 or 12 win a prize that costs you $8. Players who roll other numbers win nothing. An average of 30 guests play your game each hour, and the event will go on for 8 hours. How much money do you expect to raise during the event? Use the table below to help guide your thinking.

Roll	2, 3	4, 5, 6, 7, 8, 9, 10	11, 12
How much money you make or lose
Probability from roll

If $A$ and $B$ are mutually exclusive, then find the probability of $A$ and $B$.
The proportion of tweets made by adults in the US that are political is 33%.
1. Compute the proportion of tweets made by adults in the US that are not political.
2. You randomly read 5 tweets made by adults in the US. What is the probability that all 5 tweets are political? Assume the events are independent. Round to four decimal places.
3. You randomly read 5 tweets made by adults in the US. What is the probability that all 5 tweets are not political? Assume the events are independent. Round to four decimal places.
4. You randomly read 5 tweets made by adults in the US. What is the probability that at least one of the 5 tweets are political? Round to four decimal places.
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\(x=\) the number of semesters a student will remain in the program	0	1	2	3	4	5	6
\(P(x)\)	0.12	0.18	0.30	0.15		0.10	0.05